M719 671 Mersenne number exponent details

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	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	unknown	1650000	4141519200	6.5797	45.5341%	6.5797	45.5341%
Target	2⁴⁴	0.0000	54.5455%	12000	450000	0.0010	16.5523%	0.0010	62.0692%
Difference	-44	0.0000	-54.5455%	+1638000	+4141069200	+6.5787	+28.9818%	+6.5787	-16.5351%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
719671	35558944111	11	35.049	24705 3⁴ × 5 × 61	-	81	81	8.570e-9	2.346e-6	4.774e-6
719671	286337928607331806636426690516369	33	107.819	198936686768906768951664504 2³ × 3² × 277 × 5743 × 462437 × 965131 × 3891571	2023-01-01	965131	3891571	2.623e+11	0.0326	0.0569

exponent	prime factors	composite factor	digits	bits*
719671	35558944111 286337928607331806636426690516369	10181874400207619777017355584820259001652959	44	142.869

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 35558944111	-	-	0.037	-	-	29.475%
2023-01-01	USAFSS	6917th_Scty_Sq	1650000	4141519200			286337928607331806636426690516369	33	107.819	6.580	0.029	13.16	45.534%

ECM factoring results:

Total ECM effort:	11.328 GHz-days
Estimated T-Level:	25.658

Digits	B1	Complete	FacMiss
20	11000	14.808	0.000%
25	50000	1.620	19.795%
30	250000	0.132	87.678%
35	1000000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	6.354
250000	25000000		44	4.975

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-10-23	TJAOI	Manual testing	50000	5000000						100	2.261
2016-07-01	TJAOI	Manual testing	50000	5000000						90	2.035
2017-06-02	TJAOI	Manual testing	50000	5000000						91	2.058
2019-02-15	TJAOI	Manual testing	250000	25000000						44	4.975

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27

Oliver Kruse

GTX-1

35558944111

2037BC3702D56F__

2017-09-28

Oliver Kruse

Manual testing

35558944111

2037BC3702D56F__

2017-11-09

kkmrkkblmbrbk

c4.large

35558944111

2037BC3702D56F__

2020-04-20

Oliver Kruse

AddPrpType5

35558944111

70A4EBB926F807__

2023-01-02

LordJulius

WhiteBox

35558944111

286337928607331806636426690516369

70A4EBB926F8073D

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 1650000, B2 = 4141519200 (P-1 stage 2)

B1 = 1650000 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.7

ECM T-Level=25.66 ~= 69-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront